Level 5 NZ Curriculum Achievement Objectives for Number
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA 5-1: Reason with linear proportions.
NA 5-2: Use prime numbers, common factors and multiples, and powers (including square roots).
NA 5-3 Understand operations on fractions, decimals, percentages, and integers.
NA 5-4: Use rates and ratios.
NA 5-5: Know commonly used fraction, decimal, and percentage conversions.
NA 5-6: Know and apply standard form, significant figures, rounding, and decimal place value.
NA 5-1: Reason with linear proportions.
NA 5-2: Use prime numbers, common factors and multiples, and powers (including square roots).
NA 5-3 Understand operations on fractions, decimals, percentages, and integers.
NA 5-4: Use rates and ratios.
NA 5-5: Know commonly used fraction, decimal, and percentage conversions.
NA 5-6: Know and apply standard form, significant figures, rounding, and decimal place value.
In this unit you will revise:
1) Fractions 2) Place Value 3) Decimals 4) Integers |
In this unit you will learn:
5) Rounding using decimal places and significant figures 6) Exponents and Roots 7) Order of Operations 8) Standard Form |
CALCULATORS WILL BE ALLOWED FOR THIS UNIT
1) Fractions
A) Equivalent Fractions: Equivalent fractions are equal - they indicate the same share of a whole. A fraction wall like the one shown here can be used to find equivalent fractions. Each row is divided into the number of parts represented by the fraction. The 1/4 brick is the same length as two 1/8 bricks, so 2/8 is equivalent to 1/4.
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In order to create equivalent fractions, all you have to do is multiply the numerator and denominator by the same number
B) Comparing Fractions: In order to compare fractions (see which one is bigger) each fraction needs to have the same denominator. Therefore you must first find a common multiple for the denominators and then use this to create equivalent fractions.
C) Adding and Subtracting Fractions: Before you can add or subtract fractions, they first must have the same denominator. If they don't you will need to create equivalent fractions first. Once they have the same denominator, you add the numerators and leave the denominators the same.
2) Place Value
Our number system is called base 10. In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.
Check out this link http://interactivesites.weebly.com/place-value.html
3) Decimals
A) Adding and Subtracting Decimals:
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B) Multiplying Decimals:
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Watch this video for more help.
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C) Dividing Decimals: Dividing decimals using the algorthim is one way to solve a problem. Look at the examples below and watch the video link to help you with this.
Check out this website below for more help with decimals.
https://www.mathsisfun.com/decimals-menu.html |
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To change a FRACTION to a DECIMAL, divide the numerator by the denominator. EXAMPLE: 1/8 = 0.125
To change a DECIMAL to a FRACTION, write the digits in the numerator and the last place value is the denominator. EXAMPLE: 0.53 = 53/100 Click the image to the right to read more about changing fractions and decimals.
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4) Integers
What are integers?
- Positive and negative numbers are called integers. They have both size and direction. The number tells us the size of the measurement, and a + or - in front of the number tells us the direction of the measurement.
- ( + ) means above, right, increase, gain.
- ( - ) means below, left, decrease, loss.
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Click on the images below to have a look at INTEGER tutorials or to play an INTEGER game. Have fun!
5) Rounding
Rounding using decimal places: To round to a certain number of decimal places (d.p.), look at the digit directly to the right of the desired decimal place. If this digit is 5 for larger, the number gets rounded up. If this digit is 4 or less, the number stays the same.
Example: Round 24.548 to 2 d.p.
Since we want 2 d.p. we look at the digit in the 3rd decimal place which happens to be 8. Since this is bigger than 5 the number becomes 24.55.
Example: Round 24.548 to 2 d.p.
Since we want 2 d.p. we look at the digit in the 3rd decimal place which happens to be 8. Since this is bigger than 5 the number becomes 24.55.
Rounding using significant figures: Here are the basic rules for significant figures:
1) All nonzero figures are significant.
2) All zeroes between significant figures are significant.
3) All zeroes which are both to the right of the decimal point and to the right of all non-zero significant figures are themselves significant.
Here are some rounding examples; each number is rounded to four, three, and two significant figures.
1) All nonzero figures are significant.
2) All zeroes between significant figures are significant.
3) All zeroes which are both to the right of the decimal point and to the right of all non-zero significant figures are themselves significant.
Here are some rounding examples; each number is rounded to four, three, and two significant figures.
- Round 742,396 to four, three, and two significant figures
- 742,400 (four significant figures)
- 742,000 (three significant figures)
- 740,000 (two significant figures)
Check out these websites for more help on rounding:
http://www.purplemath.com/modules/rounding.htm
http://www.purplemath.com/modules/rounding2.htm
http://www.purplemath.com/modules/rounding.htm
http://www.purplemath.com/modules/rounding2.htm
6) Exponents and Roots
Exponents (Powers or Indices): An exponent refers to the number of times a number is multiplied by itself.
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Roots: The root of a number x is found by looking for a number that multiplies by itself a certain number of times to give the answer. For example the second root of 9 is 3, because 3x3 = 9.
The third root of 8 is 2 because 2x2x2 = 8 The second root is usually called the square root. The third root is usually called the cubed root. |
7) Order of Operations BEDMAS
Go to the website below to read more about exponents and roots and try the quiz at the end.
http://www.kids-online.net/learn/exp_root/exp_root.html
http://www.kids-online.net/learn/exp_root/exp_root.html
The accepted order of operations is remembered by the word BEDMAS. See the example to the below and click on the video if you need more help.
Check out these online sites to help you with BEDMAS
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8) Standard Form
Standard Form (Scientific Notation): This is used to write very large or very small numbers.
The number is written with decimal after the first digit and then multiplied by 10 to the
correct power.
The number is written with decimal after the first digit and then multiplied by 10 to the
correct power.